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Laws of the Iterated Logarithm for the Empirical Characteristic Function

Michael T. Lacey
The Annals of Probability
Vol. 17, No. 1 (Jan., 1989), pp. 292-300
Stable URL: http://www.jstor.org/stable/2244211
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Laws of the Iterated Logarithm for the Empirical Characteristic Function
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Abstract

Let X be a real-valued random variable with distribution function F(x) and characteristic function c(t). Let Fn(x) be the nth empirical distribution function associated with X and let cn(t) be the characteristic function Fn(x). Necessary and sufficient conditions in terms of c(t) are obtained for cn(t) - c(t) to obey bounded and compact laws of the iterated logarithm in the Banach space of continuous complex-valued functions on [ -1, 1 ].

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